How to test tables

I came across this article on designing tables for the web for 2019.

There are so many aspects of tables that we could test for, do you have any tips how?

Tables should be accessible - what tests would you do to ensure they are?
Tables should be responsive - what tests would you do to ensure they are?
Tables should display data correctly - what tests would you do to ensure they are?
Is it possible to automate some testing tasks around tables?

And so forth, would love to get some input.